A class of stochastic Gronwall’s inequality and its application

Abstract

Abstract This paper puts forward the basic form of stochastic Gronwall’s inequality and uses, respectively, the iterative method, the integral method and the martingale representation method to prove it. Then it presents an application to prove a comparison theorem of Lp $L^{p}$ solutions for one-dimensional backward stochastic differential equations under the stochastic Lipschitz condition.

Keywords

• Gronwall’s inequality
• Stochastic
• Backward stochastic differential equation
• Comparison theorem